In this talk we will discuss the stability of boundary layer and the vanishing viscosity limit of solution to compressible magneto-hydrodynamics (MHD) equations in a domain with boundary, where the velocity is imposed the no-slip boundary condition. The effects of the normal component of magnetic field, tangential component of magnetic field and magnetic diffusion on the mathematical analysis for stability of MHD boundary layer and vanishing viscosity limit of solution to compressible MHD equations will be addressed.And we also talk over some difference in the analysis of vanishing viscosity limit and stability of boundary layer between compressible and incompressible MHD equations.